21+ to 31+ γ width in Na22 and second class currents

Background: A previous measurement of the $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\gamma}$ directional coefficient in $^{22}\mathrm{Na}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$ decay was used to extract recoil-order form factors. The data indicate the requirement of a significant induced-tensor matrix element for the decay. This conclusion largely relies on a standard-model-allowed weak magnetism form factor which was determined using an unpublished value of the analog ${2}_{1}^{+}\ensuremath{\rightarrow}{3}_{1}^{+}$ $\ensuremath{\gamma}$ branch in $^{22}\mathrm{Na}$, with the further assumption that the transition is dominated by its isovector $M1$ component.Purpose: Our aim is to determine the ${2}_{1}^{+}\ensuremath{\rightarrow}{3}_{1}^{+}$ width in $^{22}\mathrm{Na}$ in order to obtain an independent measurement of the weak magnetism form factor for the $\ensuremath{\beta}$ decay.Methods: A $^{21}\mathrm{Ne}(p,\ensuremath{\gamma})$ resonance reaction on an implanted target was used to produce the first ${2}^{+}$ state in $^{22}\mathrm{Na}$ at ${E}_{x}=1952$ keV. Deexcitation $\ensuremath{\gamma}$ rays were registered with two 100% relative efficiency high purity germanium detectors.Results: We obtain for the first time an unambiguous determination of the ${2}_{1}^{+}\ensuremath{\rightarrow}{3}_{1}^{+}$ branch in $^{22}\mathrm{Na}$ to be $0.45(8)%$.Conclusions: Using the conserved vector current (CVC) hypothesis, our branch determines the weak magnetism form factor for $^{22}\mathrm{Na}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$ decay to be $|b/A{c}_{1}|=8.9(1.2)$. Together with the $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\gamma}$ angular correlation coefficient, we obtain a large induced-tensor form factor for the decay that continues to disagree with theoretical predictions. Two plausible explanations are suggested.